An extended integrable fractional-order KP soliton hierarchy

In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.